Past lecures:

Lecture 1.          Very basic properties of free groups
Lectures 2-3.     Nielsen-Schreier Theorem (subgroups of free groups are free).
Lectures 4-5.     Presentations of groups by generators and relations. Finitely and infinitely presented groups.
Lecture 6.          Residually finite groups
Lectures 7-8.     Automorphism groups of free groups.
Lecture 9.          Free products
Lecure 10.         Amalgams (briefly) and HNN-extensions.
Lecture 11.        Word growth in groups. Examples and overview.
Lectures 12-13.  Nilpotent groups have polynomial growth (Wolf's theorem).
Lecture 14.         Growth in solvable groups (Milnor-Wolf theorem)
Lecture 15.         Free Lie algebras.
Lectures 16-17.  Lie and associative rings corresponding to groups
Lecture 18.         Burnside problems. Puchta's construction.
Lectures 19-20.  Golod-Shafarevich inequality and Golod-Shafarevich groups.
Lecture 21.          Linear groups. Burnside problem for linear groups.
Lecture 22.          General Burnside problem for linear groups. Kolchin theorem.
Lecture 23.          Zariski topology. Lie-Kolchin theorem.

Upcoming lecures (plan):

Lecture 24.         Malt'sev theorem (finitely generated linear groups are residually finite).